Calculating a Normal Probability or the Area Under the Normal Curve

1. Finding :

The TI-83/84 is equiped with a built in function called normalcdf. It computes which is the area under the standard normal curve between and .

To calculate P(50 < x < 70) when = 40 and = 9, press 2nd VARS [DISTR], ARROW DOWN to select 2:normalcdf(, and then press ENTER.

After lower: type 50, after upper: type 70, after : type 40, after : type 9, and then press ENTER. See the results below.

To 4 decimal places, the P(50 < x < 70) = 0.1328.

2. Finding P(x < 70):

To calculate this probablity, P(x < 70) when = 40 and = 9, we can use the above normalcdf function since . Although we cannot enter as it is not a number, entering a very small number in its place, such as = -E99, will do.

Press 2nd VARS [DISTR], ARROW DOWN to select 2:normalcdf(, and then press ENTER. After lower: press then press 2nd [EE] and type 99. After upper: type 70, on the next line type 40, and on the next line type 9. Then press ENTER.

To 4 decimal places, the P (x < 70) = 0.9997.

3. Finding P(x > 60):

To find P(x > 60) when = 40 and = 9, use the fact that P(x > 60) = P (60 < x < ). Using E99 for , we calculate normalcdf(60, E99, 40, 9). The result is shown below.

To 4 decimal places, the P (x > 60) = 0.0131.